PHYSICS
22
PAPER-II
Time Allowed Three hours Maximum Marks 300
The figures in the margin indicate full marks for the questions
Candidates should answer Question Nos. 1 and 5 which are compulsory and any three of the remaining questions, selecting at least one from each Section
Assume suitable data if consid({red necessary and indicate the same clearly
SECTION-A
1. Answer any three of the following 20x3=60

For a particle in a one-dimensional box, discuss the zero-point energy,

show that the wave functions for two different states are orthonormal, and obtain the expectation values for x and 10=20


Apply the Schrodinger equation to the 3-D problem of the hydrogen atom to obtain the equation representing the uniform motion of the centre of mass, and the relative motion. 20


In which regions of the electromagnetic spectrum do you expect to get

rotational, vibrational and electronic spectra? Why are electronic spectra given by all molecules? State Franck-Condon principle and explain the intensity distribution in electronic spectra with the help of this principle. Give the wave-mechanical formulation of the Franck-Condon principle.


Obtain the expressions for the wave numbers of the three components (to which the original line splitted up) in the normal Zeeman effect. Show the magnetic splitting of a spectral line originating from the transition between·the two levels with l 2 and l with a diagram. Explain the origin of the anomal.ous Zeeman effect and obtain the expression for the Lande g-factor. Show, in a diagram, the anomalous Zeeman effect for sodium D1 and D2 lines.


2. What does quantum tunnelling refer to? Where does this .phenomenon find applications? How is the WKB formula used for the lifetime calculation in alpha decay? 2+2+16=20
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Find the eigenfunctions when a partiCle is kept in a rectangular box of dimensions lx x ly x lz. Find the eigenvalues of momentum and energy. Explain the term degeneracy.


Define Pauli spin matrices. How is the behaviour of the electron spin treated by Pauli's theory? What are spinors? Write a general state, and normalise it. Discuss the commutation relation between the spin operators. What is a Riemann sphere?


3. Which experiment gave a direct experimental proof of the existence of the
magnetic moment associated with the spin of the electron? Describe that
experiment in detail. What other proofwas provided by that experiment?

1+17+2=20
Explain why the state of largest L is of lowest energy. What is the
requirement for an atom in which L-S coupling and j-j coupling hold?
Consider an atom having two optical electrons with outer configuration 4p 4d. Considering L-S coupling, obtain all the terms, j-j coupling, find the possible values of J.
How does the spin-orbit interaction, when combined with the relativity
correction, explain the hydrogen fine structure? Discuss its limitations. 16+4=20
4. What is the argument for considering a diatomic molecule as an
anharmonic oscillator? Write the Morse function and the pattern of the
allowed vibrational energy levels when this function is inserted in the
Schrodinger equation. Sketch the vibrational energy levels. Show that the
zero-point energy differs slightly from that of the harmonic oscillator.
Write expressions for Lle (in for the transitions v v =1(Llv

v v (Llv and v v (Llv What are hot bands?
The following lines are observed in the absorption spectrum of HCI
2886 cm-1 (very intense), 5668 cm-1 8347 cm-1 (very·weak).
Calculate the equilibrium oscillation frequency and anharmonicity constant of the anharmonic system.
What type of scattering does the Raman effect represent? Why is Stok"es'· radiation usually more intense than anti-Stokes' radiation? Explain the Classical theory of Raman effect. Explain the statement-"Symmetric vibrations give rise to intense Raman lines; non-symmetric ones are usually weak and sometimes unobservable".
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Define luminescence. Explain fluorescence and phosphorescence with a suitable diagram. What is the approximate order of fluorescence and phosphorescence lifetimes? Differentiate between fluorescence and Raman spectra. Mention a few applications of fluorescence. 15
SECTION-B
5. Answer 'any three of the following: 20x3=60

Briefly explain the-nature of nuclear forces. What role do pions play in nuclear forces? 10+10=20


What are elementary particles? Discuss the method of their classification and their chief characteristics. 2+18=20


What is Meissner effect? How does this effect contradict Maxwell's equations? Explain the persistent currents set up inside the superconductors according to this effect. Define penetration depth. Write notes on Type I and Type II superconductors.


State De Morgan's theorem and draw the equivalent logic cirCUits. De Morganise the functions A· Band AB +C.


Simplify the given Boolean expressioq and realise an equivalent circuit using basic gates .



6. Discuss properties of the nucleus regarding its charge, mass, radius,
binding energy, spin, magnetic moment, statistics, parity and electric
moment. How is the concept of binding energy related to the stability of
the atomic nucleus? 9+11=20
Write a note on the evidence for the shell structure'of the nuclei. Discuss
the shell model of the nucleus, mentioning its achievements and failures.
. • 8+12=20
Discuss the neutrino theory of explaining the continuous energy
spectrum in [3-decay. Discuss, giving examples, different types of
[3-emission along with the conditions in which these take place. 10+10=20
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7. Mention the intrinsic quantum numbers associated with the elementary
particles, giving their corresponding conservation laws.
Conclude on the occurrence of the following reactions
p p n p 1t
p p p A0
1t P n +1t 0
A0 1t+ +1t

State the types of lattices, angles between the axes and relation between
the length of primitives for the seven classes of crystals. Explain the three
types of cubic crystals in detail. 11+9=20
Describe the model of one-dimensional periodic potential as treated by
Kronig and--Penney, and plot a curve showing the energy E as a function
of k. How the band theory lead to a possibility of a distinction
between metals, semiconductors and insulators? 16+4=20
8. What are class A and class B types of amplifiers? Mention the merits of
negative in amplifiers. Draw the circuit diagram of a two-stage
R-C coupled amplifier consisting of two single-stage transistor amplifiers
using the CE configuration. Draw its equivalent circuits in low­
frequency, mid-frequency and high-frequency ranges. Draw the
frequency response of this amplifier.
What are the characteristics of an ideal OP-AMP? What -are summing
point and virtual ground? Describe how you will use it adder,
subtractor, integrator and differentiator. Describe its use in
analog computation.
Draw the physical structure of a JFET and explain the basic operation.
Write short notes on enhancement and depletion MOSFETs. 10+10=20


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